Unicity problem on meromorphic mappings of complete Kahler manifolds
Xianjing Dong, Mengyue Liu
TL;DR
This paper extends classical Nevanlinna unicity theorems to meromorphic mappings on non-compact complete Kähler manifolds with specific curvature conditions, broadening their applicability in complex geometry.
Contribution
It generalizes Nevanlinna's unicity theorems to broader classes of Kähler manifolds with curvature constraints, a novel extension in value distribution theory.
Findings
Generalization of unicity theorems to non-compact Kähler manifolds
Applicable to manifolds with nonpositive sectional curvature
Applicable to manifolds with nonnegative Ricci curvature
Abstract
Nevanlinna's unicity theorems have always held an important position in value distribution theory. The main purpose of this paper is to generalize the classical Nevanlinna's unicity theorems to non-compact complete Kahler manifolds with nonpositive sectional curvature or nonnegative Ricci curvature.
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Taxonomy
TopicsMeromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems · Analytic and geometric function theory